Minor figure from Welsh myth; may be connected to the Gaulish god Ogmios. He also may be identified with Heueyd Hen, the father of Rhiannon.

Name & Relation to Ogmios
The spelling of "Eufydd" is a modern one; in the manuscripts, it was usually "Euuyd" or "Eueyd". The double "u" is believed to indicate a "v"--what in modern Welsh is written as "f". Likewise, the "d" in this case is actually a "ð", written "dd" in modern Welsh.

It's largely accepted that Euuyd derives from Ogmios, the Gaulish god written about by Lucian as a god of eloquence. John Rhys first suggested this connection in 1908, focusing on the mention of Eufydd in Llyfr Taliesin.

Ogmios may have been worshipped in Britain; there is a pottery shard with the name Ogmia on it, which features a figure with long curling hair and rays proceeding from his head, holding a whip (which Ross identifies with Sol Invictus).

Eufydd would also be tied to Ogma, the Irish god derived from Ogmios. Ogma is one of the figures credited with the invention of the ogham writing system; he is also not only a member of the Tuatha Dé Danann (just as Eufydd is member of Plant Dôn), but in some texts named on of the Trí Dé Dana (Three Gods of Arts?) along with the Dagda and Lugh. (And while there is no clear Welsh cognate for the Dagda, Lugh is recognizable in Eufydd's nephew Lleu.)

Texts
The name Eufydd appears in several texts, though allowance must be made for the quirks of medieval Welsh orthography. The oldest mention may be that in the poem "Prif Gyfarch Taliesin"; the Llyfr Taliesin gives the name ieỽyd, while the Llyfr Coch Hergest version has euuyd; later in the Llyfr Taliesin, in "Marwnat Aeddon", the name appears as euuyd.

The Mabinogi: in "Math vab Mathonwy", Eufydd is mentioned in the beginning as one of Math's nephews making a circuit of the land for him; in the Llyfr Gwyn Rydderch it is written as Euyd uab Dôn, and in Llyfr Coch Hergest as Eueyd uab Dôn. In most translations, his name is "corrected" to Gwydion's, as Gwydion is the focus of the story.

There are two other figures with this name in the Mabinogi--Heueyd Hen, father of Rhiannon, and Eueyd Hir, one of Bran's messengers in "Branwen uerch Lyr", who goes after Matholwch with Manawydan. He is also one of the seven advisors whom Bran leaves as regents, later murdered by Caswallawn. It's possible that all three figures are originally the same; certainly their names are close enough that Evans, in his edition of the Mabinogion, groups them together in his index.

While often written Hyfaidd Hen or Heveydd Hen in English, the original manuscripts give "Heueyd Hen"--the addition of the initial H not withstanding, it is identical to Eueyd uab Dôn, so much so that Anwyl argued:

If 'euuyd' is Eveyd Hen the father of Rhiannon, then it is not impossible that Rhiannon herself belongs to the Don-cycle, as the form of her name would suggest.

the form of her name including the divinizing element -on, also seen in the names Gwydion, Gofannon, Mabon, etc., which has its origin in the names of Gallo-Brittonic deities (such as Maponos, Epona).

As Ogmios is described as aged, hen, "aged", the apellation tied to Rhiannon's father, would be appropriately tied to Eufydd. Also, Heueyd Hen's role as an otherworld/underworld king would make an interesting parallel not only to Ogmios' role as an underworld deity, but to that of Afallach and his daughter Modron. Afallach is king of Annwfn (the Otherworld), and his daughter Modron likely a sovereignty goddess, as evident in a story where she mates with King Urien. Modron is more famously known as the mother of Mabon, the lost son, to whom Rhiannon's son Pryderi is often compared (and likely conflated). So, [H]eueyd, Rhiannon, and Pryderi form a similar family to Afallach, Modron, and Mabon.